At the end of the course, the student is able to:

Chemists rely on various analytical technologies using specific instrumentation for characterizing samples of any kind either qualitatively or quantitatively. These technologies yield data in the form of spectra or images, which often require further processing or filtering to extract the relevant information.

Fourier analysis is of great relevance in many applications in natural sciences, as many phenomena and processes are inherently periodic. The Fourier transform is one of the most used mathematical tools for the analysis and interpretation of periodic signals. This course introduces Fourier series and gives an overview of the theory underlying the Fourier transform (FT) and its use. The power of this approach will be demonstrated by discussing the application of the FT in Spectroscopy, Imaging and X-ray diffraction. During the computer labs processing of NMR, IR and MS data will be practised using the Matlab computing environment.

Microscopy is a collection of techniques aimed at visualizing objects that cannot be seen by the naked eye. Microscopic techniques yield images, which are essentially 2D datasets or signals. This course introduces the most commonly used microscopic techniques, including classical optical microscopy, phase sensitive microscopy, interferometry, fluorescence microscopy, polarized light microscopy and superresolution microscopy, transmission and scanning electron microscopy, atomic force microscopy and scanning tunneling microscopy. By treating the light or electrons either as rays or waves, both classical optics and Fourier methods can be used to visualize and measure objects. During the computer lab, image processing methods will be practiced using Matlab.